EXPERIMENTAL STUDIES ON NATURAL AND FORCED AROUND SPHERICAL AND MUSHROOM SHAPED PARTICLES.

A Thesis

Presented in Partial Fulfillment of the Requirements for the degree Master of Science in the Graduate School of The Ohio State University

by Abdullah M. Alhaxsdan

***** The Ohio State University 1989

Master's Examination Committeet Approved by Dr. Sudhir Sastry Dr. Harold Keener Dr. Santi Bhowmik

' Adviser Department of Agricultural Engineering ACKNOWLEDGEMENTS

I would like to acknowledge the guidence and support of Dr. Sudhir Sastry, advisor, and my thesis committee, Dr. Santi Bhowmik, and Dr. Harold Keener in guiding me for the research of this thesis. In addition, I appreciate my previous advisor Professor John Blaisdell, who is now retired, in supporting and helping me start this thesis. Thanks also to Mr. Dusty Bauman and Mr. Brian Heskitt for their help in lab work.

A special thanks to my wife , Jwaher, in supporting me and her patience with me. My daughter, Rehab, also is a great delight during the work in this thesis.

ii THESIS ABSTRACT

THE OHIO STATE UNIVERSITY GRADUATE SCHOOL

NAME: ALHAMDAN, ABDULLAH M. QUARTER/YEAR: SUMMER/1989

DEPARTMENT: AGRICULTURAL ENGINEERING DEGREE: M.S.

ADVISOR«S NAME: SASTRY, SUDHIR K.

TITLE OP THESIS: EXPERIMENTAL STUDIES ON NATURAL AND FORCED CONVECTION AROUND SPHERICAL AND MUSHROOM SHAPED PARTICLES.

Heat transfer coefficients (h) between fluids and particles were determined for three situations: the first two involving of a mushroom-shaped particle immersed in Newtonian and non-Newtonian liquids, and the third involving continuous flow of a sphere within liquid in a tube. For natural convection studies, h was much higher for heating than for cooling, and decreased with time as equilibration occurred. For the continuous flow studies, h was found to increase with flow rate.

Advisor's Signature VITA

February 1962 . . . Born - Riyadh, Saudi Arabia 1984 B.S. in Agricultural Engineering, King Saud University, Riyadh, Saudi Arabia 3 984-1985 T.A. In Agricultural Engineering at King Saud University

Publications Alhamdan, A., Sastry, S., and Blaisdell, J. 1988. Experimental Determination of Free Convective From a Mushroom-Shape Particle Immersed in Water. Paper No. 88-6595, Am. Soc. Agric. Eng., St. Joseph, Mich.

FIELDS OF STUDY Major Field: Agricultural Engineering, Studies in Food Processing Engineering.

iii TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii VITA iii LIST OF TABLES vi LIST OF FIGURES viii SYMBOLS x INTRODUCTION 1 CHAPTER PAGE I. LITERATURE REVIEW 4 II. THE OBJECTIVES 12 III. ANALYSIS 13 IV. PHASE 1: NATURAL CONVECTION BETWEEN A WATER AND A MUSHROOM SHAPE PARTICLE 16 Materials and methodology 16 Results and discussion 21 V. PHASE 2: NATURAL CONVECTION BETWEEN A CMC SOLUTION AND A MUSHROOM-SHAPE PARTICLE . 31 Materials and methodology 31 Results and discussion 33 VI. PHASE 3: FORCED CONVECTION OF SPHERE. . 42

IV Materials and methodolgy 43 Results and discussion...... 49 VII. CONCLUSION 37 APPENDICES Appendix A: Material properties 61 Appendix B: Sample of calculation. ... 62 LIST OF REFERENCES 71 LIST OF TABLES

TABLE PAGE

1. Average heat transfer coefficients (h), w/m K, for variable temperature differences for heating and cooling of still mushroom-shape particle immersed in still water 22 2. A summary of average Biot number, and heat parameters f and j values for mushroom-shape particle immersed in still water 22 3. Average fluid velocities (m/s) around the particle during cooling and heating the particle for different CMC solutions 35 4. Average heat transfer coefficients (h) for variable temperature differences and concentration for heating and cooling of still mushroom-shape particle immersed in still CMC solution. ... 35 5. A summary of average Biot number (Bi), and heat parameter (f) values for mushroom-shape particle immersed in still CMC solution 36

vi 6. Viscosity data (consistency coefficient "m" and flow behavior index "n" ) of CMC concentrations .5, .8, and 1.2 % at temperatures 20, 40, and 80°C. 36 7. A summary of heat transfer coefficients for moving sphere immersed in water flowing in a tube at different flow rates 1.26x10"*, 2.52x10'* , 4.42x10"*, 6.31x10"* m3/s and their slopes correlation coefficients "R" 50 8. A summary of average Biot number, and heat parameters f and j values for sphere particle flowing within fluid in holding tube at flow 1.26x10"*, 2.52x10"*, 4.42x10"*, and 6.31x10"* mVs 50 9. A comparison between the particle and the fluid velocities 56

vxi LIST OF FIGURES

FIGURE PAGE

1. Sketch of the mushroom particle , 17 2. Typical plot of temperature difference versus time and their f and j heating parameters ... 20 3. Plot of Nusselt number versus Rayleigh number for heating and cooling of mushroom-shape particle immersed in still water 23 4. Plot of Nusselt number versus Fourier number for heating and cooling of mushroom-shape particle immersed in still water 24 5. Plot of Rayleigh number versus Fourier number for heating and cooling of mushroom-shape particle immersed in still water 25 6. Plot of Nusselt number versus Rayleigh number for heating and cooling of mushroom-shape particle immersed in still CMC solution. ... 37 7. Plot of Nusselt number versus Fourier number for heating and cooling of mushroom-shape

viii particle immersed in still CMC solution. ... 38 8. Sketch of experimental system for phase 3 ... 44 9. Heat transfer coefficient versus flow rate for sphere flows within water 54 10. Nusselt number versus Reynolds number for sphere flows within water 55 SYMBOLSI

A = Surface area of the particle, m2.

Cp = Specific heat of the particle, J/(Kg K). d = Equivalent particle diameter, m.Ta = Temperature of water stream in the tube, degree C. D = Tube diameter, m. g = gravitational acceleration, m/s2. h = Heat transfer coefficient, w/m2K. K = Thermal conductivity, w/mK. m = Mass of the particle, Kg. t = time, seconds.

Tobj = Temperature of particle center during process, degree C. Ti = Initial temperature of the particle, degree C. u = water velocity in the tube, m/s. v = medium velocity around the particle due to free convection, m/s. V = Particle volume, m3. Greek Letters: a = Thermal diffusivity, m2/s. 6 = Volumetric thermal expansion coefficient, K , n = viscosity of the liquid., Poscal.sec. p = mass density, Kg/m3. r = Shear stress, N/m2. u = Kinematic viscosity, m2/s. 7 = Shear rate for non-Newtonian liquids,s'1.

Dimensionless Parameters: Re = Reynolds Number=

Pr = Prandtl Number = Cp/*/Kf

Nu = Nusselt Number = hd/Kf

Ra = Rayleigh Number = gB (Tobj-Te) <3?/ua

3 2 Gr = = gJ3(Tobj-Te)d /i'

Bi = Biot Number = hd/ks Fo = Fourier Number= at/d2

XI INTRODUCTION!

Natural and forced convection around particles are common phenomena which occur in a number of food processing applications. Agitated sterilization of soups containing vegetable particles is an example of forced convection occurring around the particles during processing. Non- agitated canned food processing is an example of natural convection from the canned fluid to its content of .

In pasteurization or sterilization of foods, it is necessary to ensure that all food particles have been processed properly, otherwise harmful effects may result. Insufficient thermal processing of foods may lead to the survival of undesirable microorganisms. Food engineers must be able to calculate and determine the proper heat treatment required to pasteurize or sterilize food particles. To avoid overcooking the food and to save energy, the heating of food particles should not exceed the proper temperature and time. However, the heating should not be less than that necessary to destroy harmful organisms. 2 In heat exchangers such as tubes and retorts, heat will penetrate from the hot medium to the food. If the food contains solid particles in a liquid, calculating the time- temperature combination required to sterilize the center of food particles requires two steps. First, it is necessary to determine the heat transfer to the liquid and then from the liquid to food particles. Heating of liquids in heat exchangers is fairly well understood; however, the most important factor that needs more investigation is to determine the heat transfer rates between fluids and particles. One of the most important parameters influencing liquid to particle heating is the convective heat transfer coefficient, which depends on variety of factors such as particle shape, fluid(medium) properties, and flow rate of the fluid passing the particle.

The emphasis in this thesis will be on the determination of convective heat transfer coefficient between liquids(the medium) and the surface of the particles; under various temperature differences, particle shapes, and fluid velocities. The research will be divided into three main phases depending on the nature of the medium (Newtonian or non-Newtonian and the position of the particle during processing (still or moving particle within the fluid). The first phase involves natural convection heat transfer between a mushroom-shaped particle and still water. 3 The second phase includes heat transfer from a still mushroom-shaped particle to still CMC solution. The last phase will be conducted to determine heat transfer parameters from a hollow sphere particle flowing within water at different velocities. The form of these studies will be the determining of convective heat transfer under transient rather than steady- state conditions. Many of the dimensionless correlations in the literature have been obtained under steady-state conditions, which are not likely to occur under actual food processing situations. Whenever appropriate, these studies will attempt to express heat transfer coefficients as time- dependent functions. CHAPTER I.

LITERATURE REVIEW

Numerous studies have involved heat transfer from fluid to particles by free or forced convection (or both). However, much of this research dealt with steady state convective heat transfer. Since the time required for processing most fluid foods is short, it is important to study and investigate the transient heat transfer of food to particles either naturally or by forced convection. Little research has been done on transient convective heat transfer. This literature review will be divided into two sections; the first is conducted for natural and forced convection of still particles immersed in fluid. The second section will include literature related to moving particles within fluid.

Natural and forced Convection of still particle immersed in wateri There is some literature written on free and forced 5 convective heat transfer from fluids to spheres and other symmetric shapes( Yuge (1960), Chen (1977), Johnson (1987), Klyacko (1963), Amato and Tien (1972), and Sastry (1984)). Most oi this literature concerns steady state heat transfer except for Sastry (1984), which deals with transient heat transfer from medium to fluid in cans and then to particles in canned foods. Yuge (1960) conducted early experimental research on combined free and forced convection heat transfer from spherical particle to air. He presented an empirical equation for free convection based on the properties evaluated at the film temperature: Nu = 2.0 + Gr"25 for 1 < Gr < 105 .-.(1) For forced convection, Yuge gave an empirical equation: Nu = 2.0 + .493 Re'5 for 10

Kirk (1984) studied combined natural and forced convection heat transfer from a sphere to air at different angles. For natural convection, Kirk's experimental results were fitted by: Nu = 0.295 Gr"286 for 3.3*105

Nu = 1.233 Gr'1735 for 1 < Gr < 108 (11) with correlation coefficient of .874, and for Forced convection: Nu = .5422 Re'5139 for 70 < Re < 3200 (12)

Sastry (1984) conducted an experiment to determine time-dependent convective heat transfer coefficients for 8 canned whole mushrooms processed in a still retort. The mean values for heat transfer coefficients ranged from 396 to 593 w/m2 C depending on sample size and temperature difference. He provided a dimensionless correlation in the form:

Nu = . 01561 (GrPr)'529 (13) with a R-squared value of .327. He also concluded that convective coefficients are influenced more by particle size than by processing temperatures. As noted from this experiment, the fluid medium temperature was not constant during processing but depends on the heat transfer rate from the retort to the liquid.

Heat transfer for solid-liquid flow in holding tubest Many articles investigated the area of continuous sterilization of liquid food containing particles either in retorts or in holding tubes. Several of these articles deal with mathematical modelling of heat transfer into particles (De Ruyter and Brunet, 1973; Manson and Cullen, 1974; Sastry, 1986; and Astrom et al., 1988). A need for experimental investigation was emphasized by several articles(Sastry(a),1987; Lenges, 1988) to verify mathematical models.

De Ruyter and Brunet (1973) attempted to treat sterilization of foods containing particulates 9 mathematically and thereby predict a heating-cooling curve for particle centers as they are processed in scraped- surface heat exchange (SSHE) equipment. • They concluded that food systems containing very small particles(less than 1/8 inch) can be treated as homogeneous for holding times of 12 seconds and over. However, in case for larger diameter, they suggested longer holding time and at lower temperature to get better results. They emphasized the need for experimental verification of the theoretical treatment. Manson and Cullen (1974) developed a mathematical model for evaluating the thermal effects of aseptically processed foods containing cylindrical particulates. They assumed a negligible surface resistance of heat transfer between the particulate and the carrier fluid. As they stated, this assumption should be tested very carefully especially for particulates that have high conductivity compare to the heat transfer to the particle surfaces. They concluded that the simulation should include the relative significance of operating parameters especially the presence of residence- time distribution (which was neglected by De Ruyter and Brunet, 1973) in the system.

Sastry (1986) developed mathematical evaluations, using finite element analysis, to determine thermal processing for low-acid foods containing particulates of any shape. He concluded that several parameters are critical to the safety 10 of the system; particle size, convective heat transfer characteristics of fluid medium, and particle residence time distribution in the and in holding tube Astrom et al (1988) developed a mathematical model to enable prediction of the quality of particulate products in a continuous heat treatment system. Their goal was to calculate the holding time required to reach a preset lethality value in the center in the fastest moving particle at the end of the process at different temperature and flow rates. They found that the effect on the food quality of a particulate product containing 20 % of 10 mm (diameter) spherical particles is greatly affected by various flow patterns. Therefore, they suggested longer holding tube to process products containing particles larger than 10 mm at low sterilization temperatures. They emphasized the necessity of experimental studies together with their model to optimize and improve product quality.

Sastry and Zuritz (1987) and Lenges (1988) had reviewed several areas related to aseptic processing. Lenges (1988) reviewed the history of aseptic processing and the major techniques used for food preservation, mainly sterilization and pasteurization. In his conclusion, he stated that among items which require more in depth studies is the bulk- sterilization of suspensions containing large particles. He emphasised that solving the area of homogeneous treatment 11 for liquid and solid phases could help to optimize the proper heating process. Sastry and Zuritz (1987) made a critical review for literature on solid-liquid flow in tubes, including capsule flow, effect on bends, radial migration phenomena, particle-particle interactions, modeling studies and other related topics. They stated that much of the information available in those topics were related to simplified flow situations. For aseptic processing systems, more realistic residence-time distribution investigations are needed to provide helpful guidelines on the sizing of holding tubes and to overcome the possibility of non uniformity in processing.

As mentioned earlier, most of the articles on continuous sterilization of food containing particulates presented mathematical solution. This thesis work emphasizes the importance of experimental investigation to determine heat transfer coefficients as attempted in this thesis. CHAPTER II.

OBJECTIVES!

1) Determine the heat transfer coefficient and other heating parameters (f and j values) for transient heat transfer between still mushroom-shape particles immersed in still water during cooling and heating processes. 2) Measure, experimentally, the heat transfer coefficient and other heating parameters of a mushroom-shaped particle immersed in non-Newtonian liquid at different viscosities and temperatures. 3) Determine heat transfer coefficients, and f and j values for heating of a sphere flowing within fluid in a holding tube. 4) Develop dimensionless correlations for each situations, as appropriate.

12 CHAPTER III. ANALYSIS

An analysis of heat transfer will be developed in order to evaluate and determine heat transfer coefficients "h" and other heating (or cooling) parameters of particles immersed in still or moving fluid. A similar analysis is used for all three phases of the present study. Analysis of heat transfer balancet Heat transfer coefficients (h), and heating parameters "f" and "j" values can be obtained by developing transient equations from an overall energy balance on the particle. In solving lumped capacitance method, as for this experiment, the first thing that should be done is to calculate the Biot number. The Biot number, which is a measure of the heat transfer by convection relative to conduction provides an indication of a uniform temperature across fie solid particle. If Bi < .1 , the resistance to conduction within the solid is much less than the resistance to convection across the fluid boundary layer (Incropera and De Witt, 1985). In the present studies, Bi < .1 was ensured

13 14 by the use of high thermal conductivity materials (aluminum) as the material for transducer. Under conditions, of Bi <.1, Newtonian heating and cooling could be used. For the heat transfer balance, the heat loss at the surface of the particle can be expressed in this equation:

q = - hA(Tobj-Ta) (14) and, the heat stored in the particle can be expressed by:

q » Cpin(dTobj/dt) (15) Thus:

q = - hA(Tobj-TB)

= mCp(dTobj/dt) (16) Rearranging , dT(t)/dt = -hA/mCp (T(t) - Te) (17) by integrating and arranging, the Newtonian law of heating and cooling is obtained:

Log (Tobj-Te) = log (Ti-T.) - (hA/mCp )t ...(18)

From the experimental data, plots of log (Tobj-T8) versus time can be made. The slopes determined using least square methods yield:

slope = - hA/mCp and y intercept = log (Ti-Ta). Therefore,

h = slope(m)Cp/A

The properties of the particle "mCp/A" and the medium are evaluated at film temperature for each temperature difference. 15

Heat Parameters "£" and "j" t Heat parameters "f" and "j" values will be used to describe the construction of cooling (or heating) curves. The "f" value is the time for a one log cycle change in driving force or, the time required for a 90 % response of the complete process. The second important parameter is the "j" value which is the ratio of the apparent initial temperature difference to the actual initial temperature difference. Both parameters are determined from heating and cooling curves basically from the plot of temperature differences versus time in semi-log scale as will be shown later.

Assumptionst 1) The characteristic dimension of the mushroom-shape particle used in this experiment is considered to be the longest diameter of the cap as shown in Fig.l. 2) The temperature within the particle is uniform since the Biot number is less than .1 (Incropera and De Witt, 1984, pp. 179). 3) For phase 1 and 2, the medium boundaries effects are negligible. 4) Radiation effect is negligible. CHAPTER IV.

PHASE 11 NATURAL CONVECTION BETWEEN A WATER AND A MUSHROOM SHAPE PARTICLE

In several food processing applications, determining the natural convection parameters needed to design the proper heat calculation to sterilize foods is very important. A typical example of this process is sterilizing canned foods containing particles. It is necessary to determine the heat transfer from food fluid to its content of particles. One of the important factors that influences this heat transfer is the heat transfer coefficient. The objective in this chapter is to investigate and measure the natural convective heat transfer coefficients and other heat parameters for still mushroom-shaped -'articles immersed in a still fluid. MATERIAL AND METHODOLOGY:

The equipment used in this experiment consisted of two water baths, a data logger , a microcomputer, and the transducer particle.

16 17 Electrical heaters were used to increase and control the temperatures of the two water baths at different but constant levels. To avoid water movement in the test liquid due to the heater pump, a water filled beaker(800 ml) was suspended in each bath. The beaker was used to prevent water movement around the particle and to reduce the vibration due to the heater pump. Both baths were insulated to reduce the heat loss. Copper-constantan thermocouples were used to measure the temperatures of water in the beakers, and the particle center. Data of temperature history was collected by a data logger interfaced with a computer. The particle was made from aluminum cast in mushroom shape. A thermocouple was embedded in the center of the mushroom particle through a hole made to the particle center as shown in the Figure 1. The hole was sealed with an epoxy resin.

d-0.02ai mN d-0.0261 m F . . A W 7= *

TWRMOCOUPLE

CROSS SECTION

006 FIGURE 1. SKETCH OF THE MUSHROOM PARTICLE 18

The particle surface was cleaned and polished before each run to prevent any collection of other material on the particle surface. The particle shape and its properties are described in Figure 1 and appendix A. The basic procedure for this experiment was to move the particle from one bath and immerse it in test liquid in the second water bath at a different temperature. The temperatures of the particle center, the two baths, and the room were monitored and recorded at .5 second interval during this process. The particle was transferred from bath to bath with care and as fast as possible to minimize the heat transfer loss from the particle to the air. This procedure of alternating movement between bath and bath permitted the collection of natural convection data for both heating and cooling. Experimental trials were performed such that the particle was heated from the initial temperatures of 20, 40, or 60 °C to the final temperature of 40, 60, or 80 °C. as appropriate.

Cooling studies were done with the particle having initial temperatures of 40, 60, and 80 °C, being cooled to 20, 40, or 60 °C as appropriate. Six replicates were made for each range of temperature of cooling and heating resulting in a total of 72 runs. 19 CALCULATIONi

Since the present study involved transient heat transfer, time dependent heat transfer coefficients were determined by analyzing the temperature history plots in short segments and calculating heat transfer coefficients over time. Each segment represents the slope of each five points of the data; and the heat transfer coefficient was calculated for each segment. The data for the first 5 seconds of the processing were deleted because of the agitation caused by immersing the particle in water. In addition, the data of temperature differences within .5 C between particle and the fluid(medium) was deleted because of the instability of object temperature. These (h) values were used to determine Nusselt number values and the average time(for each segment) to determine Fourier number. Regressions were then performed to relate Nusselt, Rayleigh and Fourier numbers.

In addition, graphs of log(TobJ—Te) versus time were plotted as shown in a typical plot in Figure(2). The average heat transfer coefficients were obtained for each complete run from these slopes along with the physical and thermal properties of the particle, and the properties of water. 20

001 21 Dimenaionlesa Numbersi Dimensionless groups, Nu, Pr, Gr, Re, and Ra associate with convective heat transfer were developed and plotted for «ach set of runs. Nu = / ( Gr,Pr ) = / ( Ra ) for free convection

RESULTS AND DISCUSSIONJ Heat transfer coefficients (h) and other heat parameters are presented in tables 1 and 2 for heating and cooling. Correlation of temperature difference versus time and dimensionless numbers (Rayleigh, Nusselt, and Fourier numbers) are plotted in Figures 3 to 5. Heat transfer coefficients: The mean values of heat transfer coefficients for heating ranged between 597 and 970 W/m2K depending on the range of temperature difference. For cooling, (h) ranged between 384 and 521 W/m2K, depending on the temperature difference ranges. Correlation coefficients for heating and cooling curves were calculated for each run using the least square method; they range between .991 and .999. Statistical comparison between those (h) values for heating and other published results (Sastry, 1984) 22

Table 1. Average heat transfer coefficients (h), w/m K, for variable temperature differences for heating and cooling of still mushroom-shape particle immersed in still water.

Temperature Heating Cooling ranges, C. h STD h STD

20-40 652a'c •f 27 384b>1 12 b J 20 60 777a,d 34 405 ' 28 20-80 786" 127 402b>k 23 40-60 674a>s 23 428bl1 28 a 40-80 811 105 395b(m 17 60-80 850a'° 50 616blh 43

a,b Mean values in the same row followed by the different letter were significantly different ( p < 0.01 ). The pairs c,d; e,f; e,g; h,i; h,j; h,k; h,l; and h,m: Mean values in the same column followed by the different letter were significantly different ( p < 0.01 ).

Table 2. A summary of average Biot number, and heat parameters f and j values for mushroom-shape particle immersed in still water.

Temp, HEATING COOLING range Bi f j Bi f j

20-40 .0770 33,.1 1 .23 .0454 54,,8 1 .13

20-60 .0918 34..3 1 .22 .0478 55,,2 1 .35

20-80 .0929 35..1 1 .50 .0475 56.,1 1 .38 23

001 24

LJ LJ 1 CD

a: en i —

N DO LJ

LxJ Q N a o o X

.3x 1 q CO ll H II 3 UJ 3 Z ? ? z UJ

ING : .ING : en o LL I ..d z O COO L HEAT ! O O er en H h 9 O I £L S •n o 001 o 25

001 26 indicates good agreement for low temperature ranges. It was found that for each run, the time dependent (h) values indicated by each segment of the slope decreased with time. This is due to the decrease of the driving force(temperature difference) during equilibration. Statistically, in most cases with .01 level of significance, increase in temperature difference resulted in higher (h) values. As shown in Table 1, heating the particle from 20 to 40 °C leads to an average (h) value of 652 W/m2K, where (h) was 777 W/m2K for heating from 20 to 60 °C. This result shows the significance of temperature difference in the values of (h) for time dependent free convection. Experimental results for most runs show, with .01 level of significance for cooling and heating, an increase in average (h) values at higher values of initial temperature but for the same temperature difference. For example, the (h) value is 850 W/m2K for heating the particle from 60 to 80 °C while it is 652 W/m2K for heating from 20 to 40 °C. This variation of (h) values may be due to the change of liquid properties for various temperatures. As shown from Table 1, there are significant variations for (h) values at the same temperature difference between heating and cooling. Statistically with a .01 level of significance, it was found that the average (h) values for 27 heating are higher(140-200%) than those values for cooling. This wide variation between heating and cooling of (h) values may be due to the orientation of buoyancy force around the fluid. For cooling the particle, because of the fluid density gradient around the particle, the heated fluid around the particle boundary rises upward. However, for heating the particle, the cooled fluid around the particle moved downward. The variation of (h) between heating and cooling may be influenced by the mushroom shape of the particle which was not uniform. It may be that the rate of the fluid movement and replacement around the particle is higher for downward (heating) than that for upward motion (cooling). The time needed to transfer the partible from bath to bath (in the experimental procedure) may also affect the difference of values for (h). When the particle was transferred from the hot bath the cold bath, heat loss from the particle to the air was higher than that from cold bath to the hot bath. This reflects the difficulty in getting a relative step input for cooling and heating. Dimensionless Correlation;

Rayleigh Number(Ra) versus Nusselt Number(Nu), Nu versus Fourier Number(Fo), and Ra versus Fo were plotted in Figures 3, 4, and 5. Power curve analysis yielded the following equations to fit the data: 28 1) Heating Process: Nu = 5.53 Ra.21 , r2=.898 (19) Nu - 6.3xlO2 Fo"'18 , r2=.982 (20) log Ra = 17.5 - 1.15 Fo , r2=.999 (21)

2) Cooling process: Nu = .08 Ral27 , rz=.898 (22) Nu = lxlO2 Fo-23 , rz=.969 (23) log Ra = 17.8 - .75 Fo , r2=.995 (24)

These correlations are valid for: 2*106 < Ra < 3*109 Figure(2) presents a typical plot of temperature difference versus time and shows how to determine heat parameters f, j from a semi-log plot. Random runs were selected to determine the construction of their cooling and heating curves using heat parameters f and j values which were presented in Table 2. It was found that for 90 % of the process responses,f were slightly slower for higher temperature difference. For 20 °C temperature difference, f value was 33.1 while it was 35.1 for 60 °C temperature difference. In addition, f value was higher for cooling than that of cooling for about 160 % which reflect the slower response for cooling compare to heating process. " j" values also increased slightly for higher temperature which 29 may reflect the instability of their initial response for the process. Figure (3) shows that the Nusselt Number increases with increasing Rayleigh Number. The data reflects a good agreement with the cooling power curves compared to those of the heating curves. The correlation coefficients were .732 for cooling data and .701 for heating data. The slope of heating curve is significantly greater than that of cooling. This reflects higher heat transfer coefficients for heating compared to those for cooling at the same temperature difference as discussed earlier. Figure (4) indicates that Nu for both cooling and heating decreases with increasing Fo. These results are as expected, since the temperature difference between the object and the fluid decrease over time. This correlation reflects that heat transfer coefficients for heating are higher than those for cooling. The correlation coefficient for the plots are .75 and .86 for heating and cooling respectively. Figure (5) shows a decrease in Ra with increasing Fo for both heating and cooling curves. These results are as expected, since the temperature difference between the particle and the fluid decrease over time. The graph indicates that Ra values are higher than those of heating. This reflects, again, slower heat transfer rate for cooling 30 than those for heating. The correlation coefficients for these plots are very high: .94 for heating and .99 for cooling slopes. CHAPTER V.

PHASE 2t NATURAL CONVECTION BETWEEN A CMC SOLUTION AND A MUSHROOM-SHAPE PARTICLE

The experiments of the previous chapter were performed for the mushroom shape particle immersed in water. Since several food liquids such as ketchup are non-Newtonian fluids , it is necessary to determine (h) and other heat parameters from the fluid to its particulates. This experiment was conducted to measure the heat transfer coefficient and other heat parameters from non-newtonian fluid to irregular shape particle.

MATERIAL AND METHODOLOGY: The equipment and the procedure of this experiment are similar to those described in the last chapter. Instead of using water as the medium liquid, Sodium carboxymethylcellulose (CMC) was used at different concentrations to simulate non-Newtonian liquid foods. A CMC powder was added to water to make three levels of concentration .2, .8, and 1.2 %. Since the viscosity of

31 32

this material is a strong function of the shear rate, a correlation of the viscosity parameters were obtained by a single-cylinder rotational viscometer equipped with a jacket to measure the viscosity parameters at the desired temperature. It was assumed and as indicated later by the viscometer that CMC solution follows the power law or the Ostwald-de Waele equation(BrodXey and Hershey, 1988) to relate shear stress (r) and shear rate (7):

n r = m7 (25) Generalized dimensionless numbers were used for non- Newtonian liquids in which the difference from dimensionless numbers for Newtonian fluid was that the viscosity term

(apparent viscosity, pt) in the latter case was reformed as a function of (m) and (n). These viscosity parameters were included in the following generalized dimensionless numbers:

1 1 1 Prg = Cpp^k(= Cp m{ (3n+l)/n} WMV " d* }/k< (26)

Grg = 2 3 1 rv1 1 - gflp (TobrT.)d /[m{(3n+l)/n>' 2 /Mv * d«-« }] (27)

or,

z 3 2 Rag=PrgGrg= gBp (T<>bl-T#)D /o/»« - gfi/tTabrT.JdVfafnUpn+lJ/n}" 2""7{4v1-t dp'1 }]2 ) (28) Where Prg, Grg, and Rag are generalized Prandtl number, 33 Grashof number, and Rayleigh number, respectively. The viscosity parameters, consistency coefficient (m), Pa.sn, and flow behavior index (n), dimensionless, of CMC solutions were measured for .5, .8, and 1.2 % concentrations and 20, 40, and 80 °C after each set of experiments. The experiments were conducted such that each concentration was used for heating and cooling process at temperature range of 20 to 40 °C and 20 to 80 °C. Six replicates were done for each set of the experiment resulting in seventy two runs in addition to the viscosity measurements. The velocity of the fluid around the particle during the process which due to the temperature difference in the CMC medium was estimated. After the runs, tiny grains were mixed with the CMC solution and a video camera was used to record the movement of these grains during the process. The average estimated fluid velocities for heating and cooling are shown in Table 3. Since the concentration of the CMC solution were relatively low, the density of CMC solutions was assumed to be equal to water density.

RESULTS AMD DISCUSSION: The average (h) for different CMC concentrations and temperature ranges for heating and cooling are summarized in Table 4. Other parameters such as Biot number and f are also summarized in Table 5. The resulting data for 34 viscosity measurement of different CMC solution and at different temperatures is shown in Table 6. A generalized dimensionless numbers as a function of temperature difference, and time were plotted in Figures 6 and 7. The average values of (h) ranged between 21 and 310 w/mzK depending on the variables: the concentration of CMC solution, temperature difference range, and heating or cooling. Statistically, with .01 level of significance, heat transfer coefficients increased with decreasing CMC concentrations. For example, decrease the concentration of CMC solution from 1.2 to .5 % resulted in increase (h) from 57 to 200 w/mK (about 400 % increase) when heating at the same temperature difference from 20 to 40 °C. In addition, increase temperature ranges cause an increase of (h) values ( h values increase from 200 to 310 w/mk correspond to increase temperature range from 20-40 to 20-80 °C). Another phenomena is the lower (h) values found of cooling than that of heating at the same temperature difference and CMC concentration as discussed in the previous chapter. Generally, the (h) values for this experiment are much less than that of water from the previous experiment which due to the present of CMC in water in the first case.

To assure that the assumption of uniform temperature occurs during process, the Biot numbers were tabulated in Table 5. 35

Table 3. Average fluid velocities (m/s) around the particle during cooling and heating the particle for different CMC solutions.

TEMP. CONCENTRATION RANGE .5 % .8 % 1.2 % .5 % .8 % 1.2 COOLING HEATING

20-40 00119 .0005 .0003 .0017 .0006 .0005 20-80 00512 .0025 .00281 .009 .0061 .0043

Table 4. Average heat transfer coefficients (h, w/m2k) for variable temperature differences and concentration for heating and cooling of still mushroom-shape particle immersed in still CMC solution.

temperature HEATING COOLING ranges .5% .8% 1.2 % .5% .8% 1.2

20-40 200a>n 148C 57e 71b>y 27.7d'9 22.1£

20-80 310g'n 1781 75k 153h>x 71.9J>r 29.11

The pairs a,b; c,d; e,f; g,h; i,j; k,l; Mean values in the same row followed by the different letter were significantly different ( p < 0.01 ). The pairs m,n; x,y; and r,s: Mean values in the same column followed by the different letter were significantly different ( p < 0.01 ). 36

Table 5. A summary of average Biot number (Bi), and heat parameter (f) values for mushroom-shape particle immersed in still CMC solution.

Temp, HEATING COOLING range .5 % .8 % 1.2 % .5 % .8 % 1.2%

20-40 Bi .05 .04 .01 .02 .007 .006 f 154 248 296 235 450 503 20-80 Bi .08 .05 .02 .04 .02 .008 f 71 191 259 225 365 707

Table 6. Viscosity data (consistency coefficient "m" and flow behavior index "n" ) of CMC concentrations .5, . 8, and 1.2 % at temperatures 20, 40, and 80 °C. CONCEN. TEMPERATURES % 20 40 80

r 1 n n m, Pa.s n m, Pa.s n m,Pa.s .5 1.072 .012 ,938 .013 1.52 .001 .8 .7402 .388 ,838 .149 1.11 :0105 1.2 .674 .921 764 .325 1.006 .0315 37

O P UJ 00 o CO q o CO i o

q

q

?o TO X 00 SO CN • q • cs n fl 3 3 Z Z I • • to NG : Lu po D o O O o o a O o i O Q: I CO (0 q co c D q q in d fe 901 38

001 39

The experiments were validated (regarding uniform temperature) since all Biot numbers are less than .1. It was found that the process time of heating and cooling in CMC solutions was very long compared to that of water as detailed in the previous chapter. This result should be reflected in food processing in which particles processed in viscous media (specially in relatively high concentrations which include most food solutions) need much longer time than that in water. The average f values (f is the time required to complete 90 % of the process) for water was 56 seconds while it is 700 seconds for 1.2 % CMC solution. In addition, the process time also depends on the concentration of the CMC solution and temperature difference; depends on those two factors, the (f) values ranged between 71 and 707 seconds.

As discussed earlier , the velocities of the liquid around the particle were roughly estimated and presented in Table 3. As expected, the average velocities resulted from the upward and downward of fluid around the particle during processing increased with increasing temperature differences and decreasing the concentration of the CMC solution. In addition, the movement of liquid around the particle was faster for heating(downward movement) than that of cooling (upward movement) which support the discussion in the 40 previous chapter that this factor contributes to the cause that heating process was higher than that of cooling. Other methods of measuring fluid movement during processing may result in more accuracy such as Hot-film anemometer sensor or using laser beam which are not available in the lab at the present time. The velocity data were used for calculation of generalized Grashof and Rayleigh numbers. Table 6 shows the viscosity coefficients: Consistency coefficient (m) and flow behavior index (n). Increased the concentration of CMC solution resulted in lower (n) and higher (m). Generally, (n) values increased and (m) values decreased as a result of temperature increase at a given CMC concentration. Therefore, it can be said that increase temperature and decrease concentration of CMC solution resulted in lower viscosity. A correlation of log Nu versus log generalized Ra was plotted in Figure 6. Increase generalized Ra resulted in increase of Nu for heating and cooling curves where Nu and generalized Ra values are higher of heating curve than that of cooling curve. The correlation can be expressed in equations (29) and (30).

For heating, 3 Nu = 1.28xlO" Rag .39 ,r2=. 971 (29) For cooling, z Nu = 7.78xlO- Rag 1.1 ,r2=. 965 (30) 41 The limitations is 4.0 < Rag< 8.0 Another correlation that relate (h) to elapsed time is the plot of log Nu versus Fo as shown in Figure 7 in which Nu decrease with time. The resulted equations are: For heating, Log Nu = 3.11-.077FO ,rz=.977 (31) For cooling, Log Nu = 1.59-.037FO ,r2=.977 (32) These results indicate the significant effects of the variation of CMC solution concentrations, temperature differences, and heating or cooling on heat transfer coefficient and process time. Those results along with experimental results of water as the medium in processing should be taken care in such design of similar food applications especially in the length of the process time. CHAPTER VI. PHASE 3t FORCED CONVECTION OF SPHERE.

The third and last phase of these experiments is the situation of continuous-flow system that simulates the actual food processing application especially of food containing particulates flowing in a tube. Temperature history of a sphere flowing in a liquid was determined in this experiment such that sphere velocity(attached to a thermocouple) simulated the actual velocity of the sphere (without the thermocouple). In this phase, an experimental procedure was developed to simulate the actual heating process of such food application. A hollow sphere was made so that its density is approximately equal to the liquid (water) density. The particle(sphere) temperature was recorded during motion within the fluid in the tube while maintaining the same velocity as that of a particle with no thermocouple attached (the free particle). Heat transfer coefficients, and f and j heat parameters were determined for flow rates 1.3xlO"\ 2.5x10"% 4.4x10"% and 6.3xlO"4 m3/s.

42 43

MATERIALS AND METHODOLOGYI A schematic of the equipment used in this experiment is shown in Figure 8. The components of the system could be divided into four sections: fluid circulating unit, data logger, materials (liquid and particle), and the devices to detect the particle velocities. Specification of the spherical particle is presented in appendix A. 1) Fluid circulating unit: This unit is the main part of the experimental equipment. It was used to circulate liquid through a tube at different velocities. Its components include: a main tube, pump, reservoir, heaters and their controller, flowmeter, and the supporting body of the unit: . The tube which was made from glass could be set and adjusted mechanically at different angles to the horizonal level. As shown in the Figure 8, the main tube had a short introductory vertical T-section permit to immersion of the particle in moving fluid. . A centrifugal pump was used to pump liquid from the reservoir to the main tube. A valve was connected at the end of this pipe to manipulate liquid flow rate. . The reservoir size which was used to store liquid is

.276 m3. . Two heaters were installed to heat the liquid in the 44

m Hi V) <

LU

LU a. 2UL o u III

00 LU Q: J5 LL 45 reservoir and connected to a digital controller to set the specified temperature by a thermocouple sensor to measure fluid temperature. . A calibrated rotameter was used to measure flow rate through the main tube over a range from 6.31xlO"5 to l.OlxlO'3 mVs.

2) Data Logger "CAMPBELL 21X MICROLOGGER": The data logger was used to record and stori output temperatures. In this experiment, thermocouples were used to measure the temperatures of the reservoir liquid, hot water bath, the room, and the particle during the process. The data logger was capable of measuring temperatures at time-intervals as low as .0125 seconds for .1 °C temperature precision. 3) The particle and the liquid: A hollow sphere made from aluminum was used as the model food particle; its outside diameter was .01825 m and inside diameter of .0149 m, and density of 1018 kg/m3. The circular ag liquid used in this experiment was water; its average properties are described in appendix A. In addition to the equipment mentioned above, the following set ups were prepared: A) Two photoelectric sensors: to measure the elapsed time between two points for a distance of 1.0 meter. The 46 first photosensor was .2 meter from the center of the introductory tube in order to avoid the data of the initial (unsteady) particle velocity. The two points of the photosensors were illuminated by light sources and photoelectric sensors for detection of the signal. As the particle flowed past the light source, it blocked the signal to the detector, actuating a timer and initiating data collection. As the particle passed through the second light source, the timer was stopped, and data logging ceased. The data logger was programmed to determine the time lag between the first and the second signal caused by the particle passing. Using this lag time and the constant distance between the sensors, the velocity of the particle was determined after each run.

B) A DC motor was used to move the particle by its thermocouple wire at a specific velocity. This velocity was set equal to the velocity of the free particle to simulate the actual particle velocity in food processing containing particles. The velocity of the motor could be adjusted to get the specified velocity but with the caution that the motor velocity was not linear with the adjustment key. C) A polyethylene cylinder(diameter=.025 M, length=.05 M) with a thin wire were used to bring back the particle from the end of the tube to the introduction port after each run. 47 PROCEDUREI The purpose of this experiment is to measure, experimentally, the heat transfer coefficient and other heat parameters of a particle flowing within a fluid (45 °C.) To overcome that the thermocouple wire attached to the particle is an obstacle to get velocity equal to the velocity of a free particle, the following procedure was developed. The procedure was divided into two major parts: first, to measure free particle velocity (within the specified fluid velocity); and second, to determine and record the temperature history of the particle attached to the thermocouple wire at the same velocity of the free particle(again, at the specified fluid velocity). Before running the experiment, the equipment was prepared to run the experiment as the following: The water in the reservoir was pumped through the tube and also heated to the specified temperature (45 °C) while a mixed of water and ice was prepared in a bath. Then, the photo sensors were placed on the tube so that the data logger recorded the steady state particle velocity and temperature history between the two photo sensors.

First, 10 replicates were done to determine the free particle velocities associated with different water flow rates. After a specified flow rate was set, the particle was dropped into the tube (through the introductory tube). 48 When the particle passed the two sensors, the data logger should record a successful run; that is, the particle passage was recorded by both sensors; otherwise the run was repeated. Ten successful replicates were done for each water flow rate required. Later, these particle velocities were used to set the velocity of the particle after it was attached to the thermocouple wire (using the motor help). The second step represented the actual process in which the particle was heated in the tube and the temperature history along with velocities data were recorded. After the velocities of all free particle runs were measured for different flow rates, the particle was opened (to two halves) and the thermocouple junction was stuck to the interior surface of the sphere. Then, the two halves are closed together by the edges of the sphere and a very thin layer of glue to prevent water leakage into the particle. After setting the specified fluid flow rate and the photosensors, the particle in the cylinder was pulled to the introductory tube. Then, the particle was placed in the ice-water beaker until particle temperature became 0.0° C(±.05° C). Gently, the particle was removed from the beaker and dropped into the main tube through the introductory tube. At the same time that the particle was removed from the beaker, the motor was turned on to start pulling the particle by the thermocouple wire until the 49 particle passes the second photosensor. After each run, it was verified that both sensors detected the particle passing, and the velocity of the particle was the same with the free particle velocity (measured in the first step). If one (or both) photosensors did not detect the particle passing, the run was repeated. In addition, care was taken to ensure that the motor speed was appropriate to pull the particle at the same velocity of the free particle; otherwise, the motor speed was adjusted until the attached particle velocity equal to the free particle velocity. When both conditions (detecting the particle and the appropriate particle velocity) were satisfied, temperature history along with particle velocity were recorded. Ten successful replicates were performed for each of the fluid flow rate resulting in 40 useful runs.

RESULTS AND DISCUSSION! The results of the average heat transfer coefficients and other heat parameters are summarized in tables 7. and 8. Table 7 showed the (h) when the particle was heated during its suspension in water from approximately 0.0 to 45 °C for different flow rates. 50

Table 7. A summary of heat transfer coefficients for moving sphere immersed in water flowing in a tube at different flow rates 1.26x10'*, 2.52x10"% 4.42x10"*/ 6.31x10"* mVs and their correlation coefficients "R". FLOW RATES, xlO* mVs Rep 1.26 R 2.52 R 4.42 R 6.31 R # 1 1310 .9407 2100 .9881 3152 .9979 2864 .9989 2 1289 .9065 2104 .9991 3028 .9932 2709 .9989 3 1407 .8868 2006 .9983 2958 .9802 3858 .9994 4 1514 .9885 2450 .9955 2887 .9952 2830 .9931 5 1310 .9407 2330 .9967 2886 .9971 2741 .9985 6 1476 .9874 2333 .9671 3094 .9931 3062 .9955 7 1351 .9689 2218 .9801 2809 .9929 3052 .9937 8 1382 .9893 225C .9804 3071 .9926 3729 .9992 9 1582 .9745 1958 .9849 3152 .9979 2879 .9989 10 1540 .9831 2195 .9981 2995 .9947 N/A

AVG 1416" 2195b.c 3003d 3080 STD 100 147 112 399 a,b; and c,d: Mean values in the same row followed by the different letter were significantly different ( p < 0.01 ).

Table 8. A summary of average Biot number, and heat parameters f and j values for sphere particle flowing within fluid in holding tube at flow 1.26x10"*, 2.52x10"*, 4.42x10"*, and 6.31x10"* mVs,

Flow rate, xlO* mVs Bi

1.26 .0155 5.21 1.04 2.52 .0241 4.33 .92 4.42 .0329 6.42 .89 6.31 .0338 3.12 .997 51

There was, statistically with .01 level of significance, a notable increase in the fluid to particle heat transfer coefficients of low flow rate compare to that of higher flow rate. For example, the average (h) values increased from 1416 w/m2K for flow rate 1.3x10'* mVs to 2195 w/m2K for flow rate of 2.5x10"* m3/s. The correlation coefficients for the run ranged between .8868 and .9994 which reflects a good agreement fitting for this experimental condition. An increase of flow rate from 1.3x10"* to 4.4x10"* mVs resulted in a doubling of the heat transfer coefficient; however, no notable statistical difference of (h) was observed between flow rates of 4.4x10' * and 6.3x10"" mVs . For all flow rates tested(except 6.3x10"* nr/s), the average temperature was 18.0 °C when the particle passed the first photosensor and 44.0 °C for the second photosensor. However, for the high flow rate of 6.3x10"* mVs the temperature of the particle was 18.0°C for the first photosensor and only 33.0° C for the second photosensor. This is more likely due to negligible increases in turbulence intensity between the two flow levels.

As noted from Table(8), generally, higher flow rates resulted in lower f values (faster response) while j values reflect a good agreement between the apparent initial 52 temperature differences to the actual initial temperature difference. In comparison between the fluid velocity and particle velocity (see Table 9), we find that they were statically similar for low flow rates 1.3x10"*, and 2.5x10" * m3/s. For higher flow rates, particle velocities were higher than average fluid velocities: 6 % for flow rate 4.4x10"* m3/s; and 11 % for flow rate 6.3x10"* mVs. The different velocities between the particle and the fluid flow was investigated in several articles (Toda (1972)). Sastry and Zuritz (1987) in their review of particle behavior in tube flow evaluated several articles for particle suspensions and for capsule flow. For our case, the particle flow in the tube may be considered as capsule flow since the particle diameter (.018 m) is almost half of the tube diameter. Sastry and Zuritz (1987) stated that Hodgson and Charles (1963) found that capsules were always moving faster than the fluid medium flow. Since the particle density used in this present experiment is similar(1018 kg/m3) to water density, it expected to be moving along the axis of the tube and therefore faster than fluid velocity. And since this study was not conducted to investigate particle behavior in tube, this explanation may give some idea about how the particle behaved in the tube. Because the particle was attached to the thermocouple during its flowing in the pipe, it is expected that the attached 53 thermocouple restricted the movement of the particle around itself compare to the free particle movement where the radial migration mostly occurred. Based on this, it is expected that the actual heat transfer coefficient may be higher than what was in this experiment which may due, as mentioned, to radial migration of particles in pipe flow phenomena which was well discussed by Sastry (1987). As expected, increase flow rate resulted in increasing of heat transfer coefficient as shown in Figure 9. This result is also illustrated in dimensionless form of Nusselt number versus Reynold number as shown in Figure 10. 54

LU

W^E3 LULL

L.CL CO(/) is < Ld JO o •y\ UJ/M «(L|) 55

301 56

Table 9. A comparison between the particle and the fluid velocities.

Flow rate, Particle velocity, Fluid velocity, m3/s m/sec m/sec

1.3x10"* .113 .1107 2.5xlO"A .223 .2213 4.4x10"* .412 .3873 6.3x10"* .628 .5533

For most food applications of heating such as pasteurization and sterilization, usually the fluid temperature is raised by a source of heat (such as steam in double tube heat exchanger), then the heat transfers to particulates in the fluid. However, for this experiment, the fluid (medium) temperature was constant with time. This may present the necessity to do an experimental work of heat transfer from fluid to particle in tube but with heating the fluid (then to its particle) during processing. This proposed experiment was done but for canned foods by Sastry (1984) in which the heat transferred from steam in a retort to the fluid in cans and then to its particulates. CHAPTERt VII.

CONCLUSION

PHASE ONE i A still mushroom-shape particle immersed in still water. 1) Mean values for the transient convective heat transfer coefficients were determined experimentally for heating and cooling. The average heat transfer coefficients ranged between 652 and 850 W/m K (depend on temperature difference range) for the heating process and 384 and 616 W/m °K for the cooling process. It was found that (h) increases by increasing temperature difference range and also by increasing the initial temperature of the particle. 2) A dimensionless correlation of the Nusselt Number versus the Rayleigh Number for heating and cooling were found to be as follows: For heating: Nu = 5.53 Ra.21

For cooling: Nu = .08 Ra*27

57 58

PHASE TWOi A still mushroom particle immersed in still non- Newtonian fluid. 1) The mean (h) were ranged between 21 and 310 w/m2K depend on the concentration of the CKC solution, temperature difference, and heating or cooling. 2) A correlation found to be: For heating, Nu = 1.28xlO"3Rag-39 For cooling, Nu = 7.78xlO"2Ragul 3) It was found that (h) was very low compared to phase 1 but the process time was relatively very long which should be considered in such design of food applications especially in holding exchangers

PHASE THREE t The sphere was moving within the fluid during heating. 1) A methodology was developed to measure (h) experimentally for a particle during its flowing in a fluid. It was obtained that the attached particle velocity was equal to the velocity of free particle. For the condition of the experiment, this study determine to what degree of flow rate can be used successfully. For flow rate 6.3x10"* mVs or higher, it was found that the particle did not process 59 adequately to the designed temperature. 2) The average heat transfer coefficient were 1416/ 2195, 3003, and 3080 w/m °K for flow rates 1.3x10"*, 2.5x10'*, 4.4x10'*, and 6.3x10"* mVs, respectively, (h) increases with increasing flow rates except for flow rate 6.3x10"* mVs which increases slightly compare to (h) at 4.4x10"* mVs. 3) Heat parameter f was found increasing with flow rates. The second heat parameter, j, was found slightly high for increasing flow rates. The assumption of a uniform temperature of the particles during processing was examined by calculating Biot number for each set of run of the three phases. As shown in tables 2, 4, and 6, the bice numbers were less than .1 which validate the assumption of this experiment.

FUTURE RESEARCH: Phase 1 and 2 * The effect of particle size, fluid viscosity, on (h) and other heat parameters should be considered to continue the work of this thesis. In addition, an experiment of liquid passing a particle at low flow rates could be benefit to determine a correlation of mixed convective heat transfer. More investigation is needed to determine the reasons for the phenomena that (h) was much higher for heating than that of cooling. 60 Phase 3 i Studies for various particle size(actually had been done in the lab but not published yet), hydraulic diameter(particle diameter to tube diameter ratio), and viscosity are needed to continue the set of this experiment. In addition, using wide range of particle densities that similar to food densities may be appropriate for this experiment. Further studies should include porous particulates to simulate some of food stuff need processing. The next possible step is to determine the heat transfer coefficient for fluid undergoing temperature increases, by steam or other media, during processing and then to its particles. These possible experiments may help more understanding and determining the processing of safe and nutritious food in an economical manner. APPENDIX:

Appendix A: Materials Properties: 1. Average water properties: K, = .628 w/m K. p - 992.3 Kg/m3. v = .ee^O"6 m2/s. a = 1.56*10"7 m2/s. 2. Average particles properties: K, = 204 watt/(m K). A = .002517 m2 for the mushroom. m = .02344 Kg for the mushroom.

Cp = .896 JcJ/(Kg K). p =2707 Kg/m3 for the mushroom. d = .028 m for the mushroom. m = .0353 Kg for the sphere d = .019 m for the sphere p = 1018.8 Kg/m3 for the sphere.

61 62 Appendix B: Sample of Calculation: THE FORTRAN PROGRAM USED TO READ THE DATA AND TO CALCULATE THE HEAT TRANSFER COEFFICIENT AND OTHER DIMENSIONLESS NUMBERS.

C TITLE :A. FORTRAN (WATFOR77 V.2) PROGRAM TO CALCULATE THE C SLOPES FOR SEVERAL LINEAEED SEGMENTS OF THE DATA C SET AND FOR THE WHOLE DATA SET, C A LINEAR REGRESSION OF TEMPERATURE DIFFERENCE VS. C TIME CALCULATE HEAT TRANSFER COEFFICIENTS FROM C THESE SLOPES AND FROM OTHER OBJECT PROPERTIES. C BY :ABDULLAH ALHAMDAN C ADVISOR :Dr. SUDHIR SASTRY C SUMMER 1989.

1 DOUBLE PRECISION YINTp,SUMYp/SUMXYp/SUMY2p, 2 R2,Rl,somx2,somy2 qo,ro2,rol, int,novy2, 3 navy2/navy2p,lltdif, m,Cp,A, BETA/ADIF,X,Y/ 4 slope,somx,somy,somxy,TfLTDIF, TDIF,te,r,u,s, 5 sumxp,sumx2p,qp,SYYNP,ba,am 14 Al(500), A2(500), TIME(500), HTC(50),SLOP,INTE 15 TROOM(500), TOBJ(500), TEQ(500),BADIF(50) 30 DATA=145 print*,'ENTER TE VALUE (79.0 TO 80.2); TE= ' READ*,TE C ** READ TEMPERATURE FILE ARRAYS: C WHERE, C A1,A2 = FORMAT SPECIFICATION FOR THE DATA C LOGGER. C TIME = DISPLAY TIME IN SECONDS FOR EACH MINUTE. C TROOM = . C TOBJ = OBJECT TEMPERATURES. C TE EQUILBRIUM TEMPERATURE. C DATA = AMOUNT OF DATA FOR EACH ARRAY IN THE C C READING FILE. C ** TEMPERATURE DIFFERENCE WILL BE WITHIN THE LIMIT OF TMAX C AND TMIN: TMAX=12.5 print*,'ENTER TMIN VALUE (.5 TO .9); TMIN= ' READ*,TMIN C OBJECT PROERTIES AT (TE+TI)/2 ARE : C Cp = SPECIFIC HEAT OF THE OBJECT, J/(Km K) C m = MASS OF THE OBJECT, Kgm. C A = SURFACE AREA OF THE OBJECT, sqr M 63

51 m=23.4377/1000. 52 Cp=.8996*1000. 53 A =25.17/10000. C *** PART I. C ** READ THE DATA FILE OF THE DATA LOGGER OUTPUT: 60 open (unit =l,file ='exp241.prn') open (unit =3,file ='exp242.prn') open (unit =4,file ='exp243.prn') open (unit =7,file ='exp244.prn') open (unit =8,file ='exp245.prn') open (unit =9,file ='exp246.prn') open (unit =10,file ='exp247.prn') 201 write(6,203) 203 FORMAT(1Ox,' OUTPUT OF THE FORTRAN PROGRAM + "AE9_PROG.FOR"'/ 3x,'FOR NATURAL CONVECTION OF A + METALLIC MUSHROOM FROM INITIAL'/3X, 'TEMP. 20.0 + TO FINAL TEMP. 40.0 C.') DO 1500 IN=1,7

70 if (IN.eq.l) read(unit=l/fmt=*)( A1(I),A2(I), + TIME(I), TOBJ(I),TROOM(I),TEQ{I),1=1,DATA) 71 if (IN.eq.2) read(unit=3,fmt=*) (A1(I), A2(I), + TIME(I), TOBJ(I),TROOM(I),TEQ(I),1=1,DATA) 72 if (IN.eq.3) read(unit=4,fmt=*)(A1(I), A2(I),TIME(I), + TOBJ(I),TROOM(I),TEQ(I),1=1,DATA) 73 if (IN.eq.4) read(unit=7,fmt=*) (A1(I),A2(I), + TIME(I),TOBJ(I),TROOM(I),TEQ(I),1=1,DATA) 74 if (IN.eq.5) read(unit=8,fmt=*) (A1(I),A2(I), + TIME(I),TOBJ(I),TROOM(I),TEQ(I),I=1,DATA) 75 if (IN.eq.6) read(unit=9/fmt=*) (A1(I),A2(I), + TIME(I)/TOBJ(I),TROOM(I)/TEQ(I)/I=1/DATA) 76 if (IN.eq.7) read(unit=107fmt=*) (Al(I)fA2(I)f + TIME(I),TOBJ(I),TROOM(I),TEQ(I),1=1,DATA) 90 close(unit=l) C ** WRITE THE ARRAYS AND THE TIME: C IF YOU WISH TO LIST THE WHOLE DATA OF THE FILE, DELETE C THE C'S PRCEEDING THE FOLLOWING STATMENTS NUMBER: c 100 do 160 I=1,G c 110 open(unit=l,file='wl') c 120 TDIF= TE - TOBJ(G) c 130 write (l,150)TIMES(G),TROOM(G),TOBJ(G),TDIF(G) c 150 FORMAT(5xff4.l,2x,f4.l,3x,f4.1,3x,i3) c 160 continue 64 c 170 close(unit=l) C *** PART II. C ** CALCULATE THE SLOPE AND THE INTERCIPT OF TEMPERATURE C DIFFERENCE VS. TIME FOR EACH PART OF THE DATA C WHERE/ LTDIF= LOG(TE-TOBJ))= LOG (TDIF). C NP AMOUNT OF DATA TO BE EXECUTED. C r TIME INITIAL, SECONDS. C u FINAL TIME, SECONDS. C s TIME INTERVAL, SECONDS. C t THE ACTUAL TIME,SECONDS C NOTE: C STATEMENTS 600, AND 610 WILL DO THE SLOPES AND OTHER C CALCULATIONS EACH FIVE POINTS OF LOG TEMERATURE C DIFFERENCE.

200 if (IN.eq.l) open(unit=ll,file='Y24.1') if (IN.eq.2) open(unit=12,file='Y24.2') if (IN.eq.3) open(unit=13,file='Y24.3') if (IN.eq.4) open(unit=14,file='Y24.4') if (IN.eq.5) open(unit=15,file='Y24.5') if (IN.eq.6) open(unit=16,file='Y24.6') if (IN.eq.7) open(unit=17,file-'Y24.7') 201 write(6,203) 203 FORMAT(1Ox,' OUTPUT OF THE FORTRAN PROGRAM + FOR NATURAL CONVECTION OF A METALLIC MUSHROOM + FROM INITIAL'/3X,'TEMP. 20.0 C. TO FINAL TEMP. + 60.0 C.'/) 204 write(6,206) if (IN.eq.l) write(ll,206) 206 FORMAT(//3x,'TABLE 1. THE SLOPES, HEAT TRANSFER + COEFFICIENT, AND CORRELATION'/12X,'FOR EACH + FIVE POINTS OF THE DATA'/ + lx,'- + '/2x, 'N + value',2x,'AVE TDIF',6X,'YINT' ,6X,'SLOPES' + ,6X'h',9X, 'R2'/lx, ' ) 210 data SUMXp,SUMYp,SUMXYp,SUMX2p,SUMY2p,TTDIF/6*0.0/ 220 NP=0 230 r=0 240 u=2.0 ii=l 241 s=.5 242 1=0 250 do 430 t=r,u,s 251 1=1+1 260 TDIF= TE - TOBJ(I) 270 if (TDIF.gt.TMAX) go to 430 65 280 if (TDIF.lt.TMIN) go to 430 330 LTDIF= DLOGIO(TDIF) 360 NP = NP+1 370 SUMXp=SUMXp+t 380 SUMYp=SUMYp+LTDIF 390 SUMXYp=SUMXYp+t*LTDIF 400 SUMX2p=SUMX2p+t*t 401 SUMY2p=SUMY2p+LTDIF*LTDIF 402 TTDIF = TDIF + TTDIF 430 continue 440 Qp=SUMXp*SUMXp-NP*SUMX2p 450 if ( QP.eq.0.0) go to 500 460 PSLOPE=(SUMXp*SUMYp-NP*SUMXYp)/Qp 461 if (NP.eq.0) go to 500 462 YINTp=(SUMYp-PSLOPE*SUMXp)/NP ADIF = TTDIF/NP BETA=.0003 BADIF(ii) = BETA*ADIF C ** CALCULATE R2 & Rl FOR SEVERAL LINEARED SEGMENTS OF C OF THE DATA SET: C WHERE, C R2 = DETERMINATION COEFFICIENT. C Rl = CORRELATION COEFFICIENT. 472 SYYNp=SUMYp*SUMYp/NP 473 R2=((YINTp*SUMYp+ PSLOPE*SUMXYp) -SYYNp) /(SUMY2p + -SYYNp) 474 Rl= SQRT(R2)

C ** CALCULATE HEAT TRANSFER COEFFICIENT FROM C SLOPES OF LOG TEMP. DIFF. VS. TIME, HTC CAN BE C DETERMEND AS FOLLOWS: 480 HTC(ii) = -1*PSLOPE*3.303*m*Cp/A 490 go to 600 500 pslope=0.0 510 yintp=0.0 530 if (pslope.eq.0.0) go to 600 if (IN.eq.2) write(12,580)NP,ADIF, YINTp,PSLOPE, + HTC(ii),R 580 FORMAT(4x,l2,4X, F8.3,3X,F8.3, 3X,F8.3, 3X,F10.3, + 5X,F7.5) 600 r=r+2.5 610 u=u+2.5 620 NP=0 630 SUMXp=0 640 SUMYp=0 66 650 SUMXYp=0 660 SUMX2p=0 641 SUMY2p=0 642 TTDIF=0 GI=DATA/5.0 if (II.gt.GI) go to 674 670 if (I.It.DATA) go to 250 write(6,673) 673 FORMATfix,'======') C NOW FROM THE DATA ABOVE, NUSSELT No. WILL BE PLOTTED C VS. RALIGHY NUNBER TO FIND THE SLPOE, INTERCIPT OF ITS c EQUATION: C FIRST, WE SHOULD DEFINE THE PARAMETERS FOR THOSE C DIMENSIONLESS No. C WHICH ARE: C GP = GRASHOF NUMBER = g*B*(TE-TOBJ)*D**3/V**2 C RE = RENOLDS NUMBER = U*d/V C PR = PRANDTL NUMBER = V/ALPHA C NU = NUSSELT NUMBER = HTC d/Kf C WHERE, C g = GRAVITIONAL ACCELERATION, M/sq.SEC. C B = VOLUEMETRIC THERMAL EXPANSION COEFFICIENT, K-l C D = CHARACTERISTIC OBJECT DIAMETER, M. C V = KINEMATIC VISCOSITY, M2/SEC. C U = FLUID VELOCITY, M/SEC. C ALPHA = THERMAL DIFFUSIVITY, M2/SEC C Kf= THERMAL CONDUCTIVITY OF THE FLUID, WATT/M.k write (6,680) 680 FORMAT(//8x,'Point #',7x,'LOG Nusselt No.',7x,'LOG Rayleigh No.'/) data SO!iX,SOMY,SOMXY,SOMX2,SOMY2/5*0.0/ NO=0 GI=DATA/5 700 do 710 ii«l,GI AM=(10.0**(12))/(0.149*0.805) if(AM.eq.0.0) go to 710 BA=BADIF(ii)*(9.81*(.05661)**3) if(BA.eq.0.0) go to 710 X=LOG10(BA*AM) Y=LOG10(HTC(ii)*(.05661/.615)) NO=NO+1 SOMX=SOMX+ X SOMY=SOMY+Y SOMXY=SOMXY+X*Y SOMX2=SOMX2+X*X SOMY2=SOMY2+Y*Y write(6,711)NO,x,y if (IN.eq.l) write(ll,711)no,x,y 67 710 continue 711 FORMAT(9x,i3,12x,f8.3,12x,f8.3) write(6,712) if (IN.eq.l) write(ll,712) 712 FORMAT (' " ' ) QO=SOMX*SOMX-NO*SOMX2 slope=0 int=0.0 SLOPE=(SOMX*SOMY-NO*SOMXY)/QO INT=(SOMY-SLOPE*SOMX)/NO C ** CALCULATE R2 & Rl FOR THE WHOLE DATA SET: 2 WHERE, C R2O = DETERMINATION COEFFICIENT. C RIO = CORRELATION COEFFICIENT. NOVY2=SOMY*SOMY/NO R2O=( (INT*SOMY+SLOPE*SOMXY) -NOVY2 ) / (SOMY2-NOVY2 ) R1O= SQRT(R2O) C ** CALCULATE HEAT TRANSFER COEFFICIENTS FOR THE WHOLE C DATA SET: SLOP=SLOPE INTE=(10)**INT 1000 write(6,1065)SLOPE,INT write(6,1051)NO if (IN.eq.l) write(ll,1065)SLOPE,INT if (IN.eq.l) write(ll,1051)NO write(6,1059)INTE,SLOP if (IN.eq.l) write(ll/1059)INTE/SLOP 1001 write(6,1063)R2O,RlO SOMX=0 SOMY=0 SOMXY=0 SOMX2=0 SOMY2=0 1051 FORMAT(//10x,' , N value = ',i5) 1065 FORMAT(//lx,'THE LINEAR EQUATION FOR THE Nu VS Ra + IS' //1X,' LOG Nu » f,f9.5,2x,f LOG Ra ',f9.5) 1059 FORMAT(/5x,'or, THE CORRELATION:', +//5X,'Nu = ',1X,F8.3,' Ra "',1X,F5.3) 1063 FORMAT(//lx,'AT: R2 =',F8.4,' AND Rl =',f8.4) write(6,1055) if (IN.eq.l) write(11,1055) 1055 FORMAT(lx,' ') 68

C *** PART III. C ** CALCULATE THE SLOPE i\12D INTERCIPT FOR THE WHOLE DATA IN THE FILE:

data SUMX,SUMY,SUMXY,SUMX2,SUMY2/5*0.0/ NT=0 1=0 do 900 tt=0,DATA,.5 1=1+1 if (I.gt.DATA) go to 900 TDIF= TE - TOBJ(I) if (TDIF.gt.TMAX) go to 900 if (TDIF.lt.TMIN) go to 900 LTDIF= DLOGIO(TDIF) NT=NT+1 SUMX=SUMX+tt SUMY=SUMY+LTD:.F SUMXY=SUMXY+t~*LTDIF SUMX2=SUMX2+t\*tt SUMY2=SUMY2+LTDIF*LTDIF 900 continue Q=SUKX*SUMX-NT*SUMX2 if (Q.eg.0.0) go to 970 TSLOPE= (SUMX*SUMY-NT*STJMXY) /Q YINT=(SUMY-TSLOPE*SUMX)/NT if (NT.eq.0) go to 970

C ** CALCULATE R2 & Rl FOR THE WHOLE DATA SET: C WHERE, C R2 = DETERMINATION COEFFICIENT. C Rl = CORRELATION COEFFICIENT. NAVY2=SUMY*SUMY/NT R2=((YINT*SUMY+TSLOPE*SUMXY)-NAVY2)/(SUMY2-NAVY2) Rl= SQRT(R2) C ** CALCULATE HEAT TRANSFER COEFFICIENTS FOR THE WHOLE C DATA SET: HTS = -l*TSLOPE*3.303*m*Cp/A go to 1010 970 Tslope=0.0 98C yint=0.0 1010 write(6/1060)TSLOPE/YINT write(6,1050)NT 69 if (IN.eq.l) write(11,1060)TSLOPE,YINT if (IN.eq.l) write(11,1050)NT write(6,1061)HTS write(6,1062)R2,Rl if (IN.eq.l) write(ll,1061)HTS if (IN.eq.l) write(ll,1062)R2,Rl SUMX=0 SUMY=0 SUMXY=0 SUMX2=0 SUMY2=0 1050 FORMAT(//10x,' , N value = #,i5) 1060 FORMAT(//lx,17X,'THE LINEAR EQUATION FOR THE WHOLE DATA IS'//1X,18X,' Y = ',fll.3,' X +',F10.3) 1062 FORMAT(//lx,17x,'AT: R2 =',F8.4,' AND Rl =',f8.4) 1061 FORMAT(//18x,'HEAT TRANSFER COEFFICIENT FOR THE WHOLE DATA IS:'//X,'HTC = ',F9.3,' WATT/sqr M K.')

C *** PART VI. C ** CALCULATE AND WRITE THE DIFFERENCE ""ERROR"" BETWEEN C THE ORIGINAL TEMPERATURE DIFFERENCE AND ITS ESTIMATED C VALUES FOR THE WHOLE DATA:

1070 pause 1080 write(6,1100) if (IN.eq.l) write(ll,1100) 1100 FORMAT(//3x,'TABLE 2. THE DATA OF OBJECT TEMPERATURE , TIME AND THE DIFFERENCE BETWEEN' /12X, 'ORIGINAL LOG TEMP. DIFFER. AND LOG ESTIMATED TEMP. DIFFER.'/I2X,'FROM THE REGRESSION'/ 3X,' ' + /4X,'DATA*',6X,'TOBJ',5X,'THE ACTUAL' ,6x, + 'ORIGINAL', 3X,'ESTIMATED',3X,'LOG + DIFF'/24X,'TIME,SECOND',5X 'VALUES OF + ',IX,'VALUES OF '/40X,'LOG TDIF',3X,'LOG + TDIFV3X,' ' ) RSUM=0.0 1=0 1120 do 1230 tt=0,DATA,.5 1=1+1 if (I gt.DATA) go to 1230 TDIF = TE - TOBJ(I) if(TDIF.gt.TMAX) go to 1230 if(TDIF.lt.TMIN) go to 1230 LTDIF= DLOGIO(TDIF) 70 YEST=TSLOPE*tt+ YINT RES = LTDIF- YEST RSUM = RSUM + RES*RES if (IN.eq.2) write(12,1220)1,TOBJ(I),tt, LTDIF, + YEST, RESfTDIF FORMAT(2X,I4,2x,f9.3,2X,f9.2,2X,f9.3,2X,f7.3,2X, + F7.3,5X,F7.3) 1230 continue write(6,1233) if (IN.eq.l) write(llf1233) 1233 FORMAT(lx,' ') write(6,1260)RSUM if (IN.eq.l) write(ll/1260)RSUM 1260 FORMAT(/20X,'RESIDUAL SUM = ',F9.3) write(6/1234) if (IN.eq.l) write(ll/1234) 1234 FORMAT(lx,'=== = '//) if (IN.eq.l) close(unit=ll) if (IN.eq.2) close(unit=12) if (IN.eq.3) close(unit=13) if (IN.eq.4) close(unit=14) if (IN.eq.5) close(unit=15) if (IN.eq.6) close(unit=16) if (IN.eq.7) close(unit=17) 1500 continue if (IN.eq.l) close(unit=l) if (IN.eq.2) close(unit=3) if (IN.eq.3) close(unit=5) if (IN.eq.4) close(unit=7) if (IN.eq.5) close(unit=8) if (IN.eq.6) close(unit=9) if (IN.eq.7) close(unit=10)

5000 stop end REFERENCES»

1) Alhamdan, A., S. Sastry, and J. Blaisdell, 1988. Experimental determination of free convective heat transfer from a mushroom-shape particle immersed in water. ASAE paper No. 88-6595. 2) Amato, W. and Chi Tien, 1972. Free Convection Heat Transfer From Isothermal Spheres in Water. International J. Heat Mass Transfer 15:327-339. 3) Astrom, A., 1988. Prediction of food quality during continuous heat treatment of particulate products. Proceeding of Food Processor Conference in Brussels, Belgium. 4) Brodkey, R. and Hershey, H. 1988. . McGraw-Hill Book Company, New York, NY. 5) Coulson, J. and J. Richardson, 1985. Chemical Engineering. Volume 1. Pergamon Press Inc., New York. 6) De Ruyter and Brunet, R., 1973. Estimation of process condition for continuous sterilization of foods containing particulates. J. Food Technology 44-51. 6) Incropera, F. and D. Witt, 1985. Introduction to Heat

71 72 Transfer. John Wiley & Sons 7nc.,New York. 7) Johnson,A., G. Kirk, T. Shih, 1987. Numerical and Experimental Analysis of Mixed Forced and Natural Convection about a sphere. ASAE paper FPE-424. 8) Kirk, G., 1984. Mixed convective heat transfer from spheres. Unpublished M. S. Thesis, Agricultural Engineering Department, University of Maryland, College Park, MD 20742. 9) Klyachko, L. S., 1963. Heat transfer between a gas and a spherical surface with the combined action of free and forced convection. J. Heat Transfer 85:355-357. 10) Lenges, J., 1988. Aseptic processing: An overview. Proceeding of Food Processor Conference in Brussels, Belgium. 11) Moon, S., 1984. Analysis of combined natural and forced convection around cylinders and spheres. Unpublished Ph.D. Dissertation, Agricultural Engineering Department, University of Maryland, College Park, MD 20742. 12) Raithby,G. , A. Pollard, K. Hollands, and M. Yovancvich, 1976. Free Convection Heat Transfer From Spheroids. ASME 452-478. 13) Sastry, S., 1984. Convective Heat Transfer Coefficients for Canned Mushrooms Processed in Still Retort. ASAE paper No. 84-6517. 73 14) Sastry, S., R. Beellman, and J. Speroni, 1985. A Three- dimensional finite element model for thermally induced changes in foods; application to degradation of agaritine in canned mushrooms. J. of Food Science 50(5):1293-1299. 15) Sastry, S., 1986. Mathematical evaluation of process schedules for aseptic processing of low-acid foods containing discrete particulates. J. of Food Science 51(5):1328-1332. 16) Sastry, S. and C. Zuritz, 1987. A model for particle suspension flow in a tube. ASAE paper No. 87-6537. 17) Sastry, S. and C. Zuritz, 1987. A review of particle behavior in tube flow : applications to aseptic processing. Journal of Food Process Engineering 10:27-52. 18) Sastry, S. , S. McCoy, and C. Zuritz, 1987. Residence time distribution of simulated food particles in a holding tube. ASAE paper No. 87-6536. 19) Sastry, S., C. Zuritz, and S. McCoy, 1987. Convective heat transfer coefficients for non-newtonian flow past food-shaped particulates. ASAE Paper No. 87-6538.

20) Yuge, T., 1960. Experiments on Heat Transfer from Spheres Including Natural and Forced Convection. J. Heat Transfer 82:214-220.